arXiv subjects

Armin Ghazi

Publications and source records attributed to Armin Ghazi.

4 recordsLinked to original sources

arXiv2026

$BMS_3$-like algebras via the $Z_N$-graded $u(1)^2$ Kac-Moody algebra

The Sugawara construction provides a natural way to construct the Virasoro algebra from a current algebra. It was shown in Ref.~\cite{Ghazi:2025oin} that for the $u(1)^2$ Kac-Moody current algebra, there exist additional constructions that exhibit a $\mathbb{Z}_N$-graded structure. Indeed, the space of such constructions defines a non-compact algebraic variety whose dimension depends on $N$. In this paper, we consider the compactification of these algebraic varieties by adding points at infinity to the non-compact part, and show that these points correspond precisely to generalizations of $BMS_3$-like algebras. More explicitly, for a $\mathbb{Z}_2$ grading, the corresponding algebra coincides with the $BMS_3$ algebra, which takes the form $\mathrm{Vir} \rtimes F$, where $F$ is an infinite abelian ideal of the full algebra. For $N > 2$, we show that there exist generalizations of the standard $BMS_3$ algebra of the form $\mathrm{Vir} \rtimes F$, where $F$ is a nonabelian ideal that forms a nilpotent algebra of depth $r < N$. We further demonstrate that the depth of the algebra is related to the order of the singularity of the algebraic variety at that point. We also show that the polynomials defining the algebraic varieties exhibit a factorization property into linear factors, which, if true, classifies all $BMS_3$-like algebras. Finally, we study the central extensions of these algebras, which are consistent with the general structure of algebras corresponding to primary fields of conformal weight $h = 2$.

hep-th↗

arXiv2025

The $Z_N$ equivariant Virasoro algebra via alternative Sugawara constructions

In this paper, we study the $U(1)^2$ Kac--Moody algebra and generalize the standard Sugawara construction of the Virasoro algebra to an infinite family of new realizations. In this case, in addition to the standard invariant tensor $δ^{ij}$, there exists another invariant tensor $ε^{ij}$, which enables the construction of genuinely new realizations beyond the conventional one. We show that these new realizations arise from a $\mathbb{Z}_N$--grading of the mode index $n$ of the Virasoro generators $L_n$ and the space of such realizations corresponds to points of a possibly singular algebraic variety. For the $\mathbb{Z}_2$ and $\mathbb{Z}_3$ cases, the space of all such constructions is topologically equivalent to a cylinder, while for $\mathbb{Z}_4$ it forms a non-compact real four-dimensional manifold. We show that the spaces of constructions for $Z_{2N}$ and $Z_{2N+1}$ are closely similar. Furthermore, we reformulate the problem within an action-principle framework by introducing $\mathbb{Z}_N$-equivariant maps, which provide a systematic method for constructing conformal field theories endowed with these generalized Virasoro symmetries. This formulation reproduces the $\mathbb{Z}_2$ case and supports the idea that $\mathbb{Z}_N$-equivariance offers a consistent and unified approach to generating extended conformal algebras. Finally, we analyze the corresponding Virasoro--Kac--Moody-like algebras associated with these constructions and show that they represent nontrivial deformations of the well-known Virasoro-Kac-Moody algebra.

hep-th↗

arXiv2024

Material and size dependent corrections to conductance quantization in anomalous Hall effect from anomaly inflow

In quantum anomalous Hall (QAH) systems, the Hall conductance is quantized and the corresponding effective topological theory of the system is the Chern-Simons theory. The conductance quantum is given by the universal constant $e^2/h$ -- the inverse von Klitzing constant -- that is independent of the bulk gap, as well as the size of the system. This picture relies on the assumption that the edge modes are sharply localized at the edge, i.e. they have zero width. We show that considering the physical case where the edge modes have finite localization length $b$, the effective action would not be topological in bulk direction anymore. Due to non-zero $b$ the conductance quantum will be corrected as $(1-\varepsilon)e^2/h$ where $\varepsilon$ encompasses the non-universal (i.e. material/sample dependent) part that is determined by the dimensionless ratios $\frac{gb}{\hbar v_F}$ and $\frac{b}{L}$ where $g,v_F,L$ are the bulk gap, Fermi velocity and sample length. To compute the non-universal correction $\varepsilon$ we use anomaly inflow framework according to which the bulk action produces the correct amount of anomaly inflow that would cancel the anomaly of the chiral edge modes. These corrections place limits on the precision of measurable quantization in units of the inverse von Klitzing constant for QAH systems with smaller sizes and/or smaller bulk gaps. Our result suggests that the failure of precision measurements to reproduce the exact conductance quantum $e^2/h$ is not an annoying sample quality issue, but it contains the quantitative physics of anomaly inflow that can be inferred by the systematic study of such corrections.

cond-mat.mes-hall↗

arXiv2019

Magneto-transport in an anomalous fluid with weakly broken symmetries, in weak and strong regime

We consider a general system with weakly broken time and translation symmetries. We assume the system also possesses a $U(1)$ symmetry which is not only weakly broken, but is anomalous. We use the second order chiral quasi-hydrodynamics to compute the magneto-conductivities in the system in the presence of a weak magnetic field. Analogous to electrical and thermoelectric conductivities, it turns out that the thermal conductivity is identified with a coefficient which depends on the mixed gauge-gravitational anomaly. By applying our general formulas to a free system of Weyl fermions at low temperature limit $T\ll μ$, we find that our system is Onsager reciprocal if the relaxation in all energy, momentum and charge channels occurs at the same rate. In the high temperature limit $T\gg μ$, we consider a strongly coupled $SU(N_c)$ gauge theory with $N_c\gg1$ in the hydrodynamic limit. Its gravity dual is a magnetized charged brane to which, we apply our formulas and compute the conductivities. On the way, we show that analogous to the weak regime, an energy cut-off emerges to regulate the thermodynamic quantities. From this gravity background we also find the coefficients of chiral magnetic effect in agreement with the well-known result of the Son-Surowka.

hep-th↗